Zonal Shear Flows with a Free Surface: Hamiltonian Formulation and Linear and Nonlinear Stability

Details Zonal Shear Flows with a Free Surface: Hamiltonian Formulation and Linear and Nonlinear Stability Zonal Shear Flows with a Free Surface: Hamiltonian Formulation and Linear and Nonlinear Stability

2007-08-24

arxiv.org/abs/0708.3383v1

Physics

Fluid Dynamics

Scientific paper

General theoretical results via a Hamiltonian formulation are developed for zonal shear flows with the inclusion of the vortex stretching effect of the deformed free surface. These results include a generalization of the Flierl-Stern-Whitehead zero angular momentum theorem} for localized nonlinear structures on or off the beta-plane, and sufficient conditions for linear and nonlinear stability in the Liapunov sense - the latter are derived via bounds on the equilibrium potential vorticity gradient.

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